mathematics
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LANS

LANS Publications

"Applications and Algorithms for Mixed Integer Nonlinear Programming"

S. Leyffer, J. Linderoth, J. Luedtke, A. Miller, and T. Munson

Journal of Physics: Conference Series, vol. 180, no. 1, , pp. 012014. Also Preprint ANL/MCS-P1630-0509

Preprint Version: [pdf]

The mathematical modeling of systems often requires the use of both nonlinear and discrete components. Discrete decision variables model dichotomies, discontinuities, and general logical relationships. Nonlinear functions are required to accurately represent physical properties such as pressure, stress, temperature, and equilibrium. Problems involving both discrete variables and nonlinear constraint functions are known as mixed-integer nonlinear programs (MINLPs) and are among the most challenging computational optimization problems faced by researchers and practitioners. In this paper, we describe relevant scienti c applications that are naturally modeled as MINLPs, we provide an overview of available algorithms and software, and we describe ongoing methodological advances for solving MINLPs. These algorithmic advances are making increasingly larger instances of this important family of problems tractable.